for most freshwater aquatic plants, each need at least 6 square in. of space and they usually hook on to the floor by grabbing the gravel.
It's not hard to move them. Just scoot your hand around the plant until you hit it's base, scoot your whole palm under and pull up.

Some plants you can just pull up with no problem at all but what i said previously is just in case.

Well some of the basics:
Stem plants like Anacharis, worts, bacopa and similar have a small root base, mine normally get a root wad about the size of a silver dollar if not smaller.
Crypt have a more extensive root system and need room because they do not like competition. Keep other root type plants away from them the best you can so they compete with the crypts for nutrients. The 3 species I have kept got a root mass about 4 inches wide when growing well.
Swords need a lot of room. The root system will grow as wide as the plant will so they can easily grow to the point where they have roots across a huge area of the tank. They will make a huge mess when pulled up.

Do you need to give them their own space, yes and no. If the substrate is a rich one like Eco Complete then you can get away with crowding mopre than if you have gravel.